1985 AHSME Problems/Problem 23
Contents
Problem
If and , where , then which of the following is not correct?
Solution 1
Notice that and . We have .
We also have .
Finally,
.
Let . We have
.
For , so
.
Therefore, for , and
, so .
As a check, we have for , and
.
Finally, for we have , and
, and this is true for all other answer choices.
Solution 2
Note that and that $y=\cos(-\frac{2\pi}{3})+i\sin(-\frac{2\pi}{3})=\cos(\frac{2\pi}{3})-i\sin(\frac{2\pi}{3})
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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